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Explore the dynamics of combined efforts: A completes the task in 15 days with 8-hour shifts, B does it in 10 days with 9-hour shifts. Calculate the duration required for both, working 8-hour shifts jointly, to finish the task.
A can complete a work in 15 days working 8 hours a day B can complete the same work in 10 days working 9 hours a day. If both A and B work together, working 8 hours a day, In how many days can they complete the work?
They can complete the work in 8 days when working together for 8 hours a day.
Work done by both A and B in 6 hours:
- Work done by A in 6 hours = 6/120 = 1/20
- Work done by B in 6 hours = 6/80 = 3/40
- Total work done in 6 hours = (1/20) + (3/40) = (2 + 3)/40 = 5/40 = 1/8
So, they complete 1/8 of the work in 6 hours.
Since they’re working together for 8 hours a day, they will complete 1/8 of the work each day.
Therefore, the total number of days required to complete the work is 1/(1/8) = 8.
Thus, they can complete the work in 8 days when working together for 8 hours a day.
Time and Work in Mathematics
Time and Work problems are a common type of mathematical question that involve calculating how long it takes for a certain number of workers to complete a task, or determining how many workers are needed to complete a task in a given amount of time. These problems typically involve the concepts of rates and proportions.
Here are some key concepts and steps to solve Time and Work problems:
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Understanding the Problem: Read the problem carefully to understand what needs to be done, what the task is, and what information is provided.
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Identify Variables: Identify the variables involved, such as the number of workers, the time taken, and the amount of work to be done.
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Formulate Equations: Based on the given information, formulate equations or expressions that represent the relationship between the variables.
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Solve for the Unknown: Use the equations to solve for the unknown variable, whether it’s the time taken, the number of workers needed, or the rate of work.
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Check the Solution: Always check your solution to ensure it makes sense in the context of the problem.
Here are a couple of common types of Time and Work problems:
Type 1: One Task, Different Workers: In this type, the problem typically involves one task to be completed, and different workers have different rates of work. You’ll need to calculate how long it takes for all the workers to complete the task together.
Type 2: Fraction of Work Done: Sometimes, the problem might involve workers leaving the job before it’s completed, or joining in after it’s started. You’ll need to calculate what fraction of the work is done by each worker or group of workers.
Example: Let’s say it takes 6 hours for a machine to fill a tank. If two machines are working simultaneously, how long will it take for them to fill the tank?
Solution: Let the work done by one machine in one hour be 1/6 of the tank’s capacity. So, the work done by two machines in one hour will be 2×1/6=1/3of the tank’s capacity. Therefore, it will take 3 hours for two machines working simultaneously to fill the tank.
These are just basic examples, and Time and Work problems can vary in complexity. It’s essential to understand the principles and apply them accordingly to solve such problems effectively.
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Source: Math Hello Kitty
Categories: Math
